document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183953>Question 183953</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780078738302/algebrahomeworkh>Glencoe McGraw-Hill: Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I hope I am submitting this problem under the right section, the chapter I'm currently studying has asymptotes so..\r<BR>\n" );
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document.write( "Haha, I've tried this problem so many ways! I feel that the mistake is right under my nose, but I still can't seem to find it. the dashes are fractions.\r<BR>\n" );
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document.write( "4/z-2 - z+6/z+1 = 1\r<BR>\n" );
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document.write( "I go to a private school, but I am currently being homeschooled for a couple weeks. My teacher wanted us to solve this problem by clearing the fractions.\r<BR>\n" );
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document.write( "Here's my most \"unjumbled\" work:\r<BR>\n" );
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document.write( "*original problem*\r<BR>\n" );
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document.write( "LCD: (z-2)(z+1)\r<BR>\n" );
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document.write( "(z-2)(z+1)/ 1  times 4/(z-2) minus (z-2)(z+1)/1 times (z+6)/(z+1) = (z-2)(z+1)/1 times 1.\r<BR>\n" );
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document.write( "4z+4-(z-2)(z+6)=(z-2)(z+1)<BR>\n" );
document.write( "4z+4-z^2+6z-2z-12= z^2+z-2z-2<BR>\n" );
document.write( "4z+4-z^2+4z-12 = z^2-z-2<BR>\n" );
document.write( "-z^2+8z-8 = z^2-z-2<BR>\n" );
document.write( "eliminate -z^2+8z-8 on the left side, do the same to the right side like...\r<BR>\n" );
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document.write( "0 = z^2-z-2<BR>\n" );
document.write( "   +z^2-8z-8<BR>\n" );
document.write( "_______________  equals\r<BR>\n" );
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document.write( "0 = 2z^2-9z-10<BR>\n" );
document.write( "not factorable, so I used quadratic formula<BR>\n" );
document.write( "a=2, b=-9, c=-10\r<BR>\n" );
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document.write( "quadratic formula: [-b (+ or -) sq. root of: b^2 - 4ac] divided by 2a\r<BR>\n" );
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document.write( "=[9 (+ or -) sq. root of: (-9)^2 - 4(2)(-10)] all divided by 4.\r<BR>\n" );
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document.write( "= [ 9 (+ or -) sq. root of: 161] all divided by 4.\r<BR>\n" );
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document.write( "my textbook says that the correct answer should be:<BR>\n" );
document.write( "[ 1 (+ or -) sq. root of: 145] all divided by 4.\r<BR>\n" );
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document.write( "Mmm.. hopefully this is readable. Please help, it's driving me bonkers! Thanks!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137997 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=137997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4/z-2 - z+6/z+1 = 1<BR>\n" );
document.write( "4(z+1)-(z+6)(z-2)=(z+1)(z-2)<BR>\n" );
document.write( "4z+4-(z^2+4z-12)=z^2-z-2<BR>\n" );
document.write( "4z+4-z^2-4z+12=z^2-z-2<BR>\n" );
document.write( "-z^2+16=z^2-z-2<BR>\n" );
document.write( "-2z^2+z+18=0<BR>\n" );
document.write( "z=(1-sqrt(145))/4, z=(1+sqrt(145))/4<BR>\n" );
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document.write( "Ed<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B1x%2B18+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B1x%2B18+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%281%29%5E2-4%2A-2%2A18=145 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%281%29%5E2-4%2A-2%2A18=145\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=145 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-1%2B-sqrt%28+145+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-1%2B-sqrt%28+145+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%281%29%2Bsqrt%28+145+%29%29%2F2%5C-2+=+-2.76039864469807 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+145+%29%29%2F2%5C-2+=+-2.76039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%281%29-sqrt%28+145+%29%29%2F2%5C-2+=+3.26039864469807 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%281%29-sqrt%28+145+%29%29%2F2%5C-2+=+3.26039864469807\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B1x%2B18 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B1x%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2x%5E2%2B1x%2B18+=+%28x--2.76039864469807%29%2A%28x-3.26039864469807%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B1x%2B18+=+%28x--2.76039864469807%29%2A%28x-3.26039864469807%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -2.76039864469807, 3.26039864469807.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B1%2Ax%2B18+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B1%2Ax%2B18+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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